What sculpting tools would I use to separate a jaw from the skull?
There is the Boolean Modifier in Blender. It's can be used to separate, merge, and cut off parts of objects/meshes. In your case, you can easily cut the lips and create an oral cavity with it. Then use the Pose brush to open the mouth.
Separate the lips
First, create a &quot;knife&quot;. For this, switch to Object Mode (CTRL + TAB). Add a plane (SHIFT + A). Add a Solidify modifier to add some thickness. (The modifiers are located on the right side. Click the blue wrench icon.) Add the Solidify modifier, adjust the Thickness, then apply the modifier (in Blender 2.9, you need to press the little arrow on the right side of the modifier's name). Then scale and rotate the &quot;knife&quot; so you can place it between the lips of your dino head. Use S to scale. While scaling you can (for example) press X to restrict the scale to the X-axis. Use R to rotate, and G to move it around.

Now cut the lips apart. To do so, place the &quot;kife&quot; right at the beginning of the dino's lips between them where you want to separate them. Select the dino's head. Add the Boolean modifier to the head. In the modifier's options select the plane (&quot;knife&quot;) as Object value, use the default mode Difference to cut out geometry. Apply the modifier. After that, move the knife a bit further along the lips into the head, apply again a Boolean modifier. Repeat these steps again if needed until you have cut the full length of the lips.

Create the oral cavity
This is very easy to do. Still in Object Mode, just add a sphere, scale it and place the dino's head where the cavity should be. Then select the head, and apply a Boolean modifier with the sphere as Object value and mode Difference.
Open the mouth
Switch to Sculpt mode. Use the Mask brush to mask the upper jaw of the head. This prevents that this area is affected by brushes. Then use the Pose brush with big size to move the lower jaw down. This part is a bit tricky since it still can happen that some vertices from the upper jaw are dragged down. Try to hide the masked area or use the Pose brush at a different spot or angle.

In the Sculpt menu you can hide masked areas and reveal them again.
The added geometry (cavity) has a lower vertex count. Switch on Wireframe overlay or to Edit mode to check it. You can use the Remesh in Sculpt Mode, or activate DynTopo and touch the area with the Clay brush and a very low strength to add needed geometry when you want to sculpt details there.